Classicality concept test on neutral pseudoscalar meson qubits with Wigner inequalities

In this study, we introduce the concept of classicality and derive Wigner inequalities that depend on two instants, with a potential extension to three instants. We explore the experimental feasibility of testing the violations of these inequalities in both pure and mixed flavor states of ${K}^{0}\ensuremath{-}$, ${D}^{0}$-, and ${B}_{s}$- meson pairs. Using the Werner noise model, we demonstrate that violations of time-dependent Wigner inequalities can be detected even when background processes constitute up to 50% of the system.